Question

Describe the following sequence as arithmetic, geometric or neither. 2, 4, 8, 16, 32. . . .

Answer 1

Answer:

Geometric

Step-by-step explanation:

Since, a sequence is arithmetic if there is a common difference in the successive terms,

While it is geometric if there is a common ratio in successive terms,

Here, the given sequence,

2, 4, 8, 16, 32..................,

Since, 4 - 2 ≠ 8 - 4 ≠ 16 - 8 ≠ 32 - 16........

⇒ There is not a common difference in successive terms,

Hence, the given sequence is not arithmetic.

Now,

$\frac{4}{2}=\frac{8}{2}=\frac{16}{8}=\frac{32}{16}.......=2$

⇒ There is a common ratio in successive terms,

Hence, the given sequence is a geometric sequence.

Answer 2

That is a geometric sequence.